การวิเคราะห์การสั่นสะเทือนเชิงตัวเลขสำหรับคานเซลลูล่าร์ที่ใช้วัสดุเชิงประกอบแบบ FGM

Authors

  • ชนนฐ์ยวัส รัตนวิเชียร นักศึกษา, หลักสูตรวิศวกรรมศาสตรมหาบัณฑิต สาขาวิศวกรรมโครงสร้าง คณะวิศวกรรมศาสตร์ มหาวิทยาลัยเทคโนโลยีราชมงคลธัญบุรี, คลองหก คลองหลวง ปทุมธานี 12110
  • กำธรเกียรติ มุสิเกต อาจารย์, ภาควิชาวิศวกรรมโยธา สาขาวิศวกรรมโครงสร้าง คณะวิศวกรรมศาสตร์ มหาวิทยาลัยเทคโนโลยีราชมงคลธัญบุรี, คลองหก คลองหลวง ปทุมธานี 12110
  • บุญชัย ผึ้งไผ่งาม อาจารย์, ภาควิชาวิศวกรรมโยธา สาขาวิศวกรรมโครงสร้าง คณะวิศวกรรมศาสตร์ มหาวิทยาลัยเทคโนโลยีราชมงคลธัญบุรี, คลองหก คลองหลวง ปทุมธานี 12110

Keywords:

Bi-Directional Functionally Graded Material, Cellular Beam, Finite Element Method, Vibration, Natural Frequency, Mode Shape

Abstract

This research performs a freeform numerical vibration analysis for a two-dimensional problem using the Finite Element Method of a cellular Euler-Bernoulli beam with mechanical material properties. BDFGM (Bi-Directional Functionally Graded Materials) is composed of two materials, Aluminum and Zirconia. A mixing law based on rule of mixtures is proposed to account for the variation in the volume fraction of materials. It is determined that the variation indices of elastic modulus and density vary with the exponentially along the axial direction and power law with the depth of the beam. The first three natural frequencies of the simple cellular beams obtained from the analysis are found to be inversely proportional to the variation index increasing in both directions with the variation index increasing with depth. It affects the rate of decrease of the natural frequency value more than the axial variation index. This proposed model can be applied to the analysis and design of bidirectional composites consisting of more than two materials with different properties in order to determine the appropriate natural frequency value for the desired problem.

References

Kobayashi Y, Harada A, Yamada G. Reduced-order nonlinear modal equations of plates based on the finite element method. JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing. 2002;45(1):79-86.

Sina SA, Navazi HM, Haddadpour H. An analytical method for free vibration analysis of functionally graded beams. Materials & Design 2009;30(3):741-7.

Simsek M, Kocaturk T. Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Composite Structures 2009;90(4): 465-73.

Gao K, Li R, Yang, J. Dynamic characteristics of functionally graded porous beams with interval material properties. Engineering Structures 2019;197:109441. doi: 10.1016/j.engstruct.2019.109441.

Nguyen N, Nguyen T, Nguyen T, Vo T. A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams. Composite Structures. 2022;282:115095. doi: 10.1016/j.compstruct.2021.115095.

Al-Zahrani MA, Asiri SA, Ahmed KI, Eltaher MA. Free vibration analysis of 2D functionally graded strip beam using finite‎ element method‎. Journal of Applied and Computational Mechanics 2022;8(4):1422-30.

Sharma NK, Bhandari M, Dean A. Applications of functionally graded materials (FGMs). International Journal of Engineering Research & Technology 2014;2(3):334-9.

Wang M, Zhang P, Fei Q. Computational evaluation of effects of fiber shape on transverse properties of polymer composites considering voids under dynamic loading. Journal of Aerospace Engineering 2019;32(4):04019049.

Taraghi P, Showkati H, Firouzsalari SE. The performance of steel conical shells reinforced with CFRP laminates subjected to uniform external pressure. Construction and Building Materials 2019;214:484-96.

Mahamood RM, Akinlabi ET. Functionally graded materials. Topics in Mining, Metallurgy and Materials Engineering. Cham, Switzerland: Springer; 2017. doi: 10.1007/978-3-319-53756-6_2.

Nejad MZ, Hadi A. Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams. International Journal of Engineering Science 2016;105:1-11.

Li X. A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. Journal of Sound and vibration 2008;318(4-5):1210-29.

Musiket K, Phungpaingam B, Piyaphipat S. Free and forced vibration analyses by n-sided polygonal cell-based strain-smoothed finite element for two-dimensional problem. RMUTP Research Journal Sciences and Technology 2023;17(2):53-66. (In Thai)

Simsek M. Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions. Composite Structures 2015;133:968-78.

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Published

2024-12-25

Issue

Vol. 14 No. 3 (2024): September-December 2567

Section

บทความวิจัย (Research Article)

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